Newton and Secant Methods: Problems and Solutions

A method to address general problems in Newton's method (and its other version, the secant) including a division by zero and oscillation.

https://www.researchgate.net/publication/358857049_A_Method_to_Avoid_the_Division-by-Zero_Situati...

Version 1.2.3 (925 KB)
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20 Mar 2022

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Newton's method is a powerful approach to solving nonlinear equations but it fails (also its approximate, the secant) when the derivative of the function equals zero, approaches zero (diverges or converges very slowly), or due to oscillation between two or more estimates. The attached method provided with six examples programmed in MATLAB shows some methods to avoid such situations.

Cite As

Ismael Abdulrahman (2026). Newton and Secant Methods: Problems and Solutions (https://uk.mathworks.com/matlabcentral/fileexchange/107260-newton-and-secant-methods-problems-and-solutions), MATLAB Central File Exchange. Retrieved .

General Information

MATLAB Release Compatibility

  • Compatible with any release

Platform Compatibility

  • Windows
  • macOS
  • Linux
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Version Published Release Notes
1.2.3

Minor update.
1.2.2

Additional files, examples, and programs.

1.2.1

A total of six examples are provided, each is solved using three methods when the standard Newton's method fails to solve.

1.1.9

Minor changes.

1.1.8

Improvements.
1.1.7

Adding two new examples.
1.1.6

Minor
1.1.5

Minor
1.1.4

Minor
1.1.3

Minor
1.1.2

Minor improvements.

1.1.1

Minor improvements.

1.1.0

Improvements, new methods, and additional examples from a textbook. The case of division by near-zero is added from a textbook.

1.0.7

Minor
1.0.6

Minor
1.0.5

Minor
1.0.4

Minor
1.0.3

Minor
1.0.2

Minor change
1.0.1

Minor change.
1.0.0